Linear Convergence of Epsilon-Subgradient Descent Methods for a Class of Convex Functions

Robinson, S.M. (1996). Linear Convergence of Epsilon-Subgradient Descent Methods for a Class of Convex Functions. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-96-041

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Abstract

This paper establishes a linear convergence rate for a class of epsilon-subgradient descent methods for minimizing certain convex functions. Currently prominent methods belonging to this class include the resolvent (proximal point) method and the bundle method in proximal form (considered as a sequence of serious steps). Other methods, such as the recently proposed descent proximal level method, may also fit this framework depending on implementation. The convex functions covered by the analysis are those whose conjugates have subdifferentials that are locally upper Lipschitzian at the origin, a class introduced by Zhang and Treiman. We argue that this class is a natural candidate for study in connection with minimization algorithms.

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